The dynamic spin structure factor $mathcal{S}(k,omega)$ of a system of spin-1/2 bosons is investigated at arbitrary strength of interparticle repulsion. As a function of $omega$ it is shown to exhibit a power-law singularity at the threshold frequency defined by the energy of a magnon at given $k.$ The power-law exponent is found exactly using a combination of the Bethe Ansatz solution and an effective field theory approach.
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